Geometry Proof - Parallel Lines

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Homework Help Overview

The discussion revolves around a geometry proof involving parallel lines and angle congruence. The original poster presents a scenario where two lines are given as parallel, along with two angles that are congruent, and seeks to prove another pair of lines are also parallel.

Discussion Character

  • Exploratory, Assumption checking, Conceptual clarification

Approaches and Questions Raised

  • Participants explore the implications of the given information regarding angle congruence and parallel lines. There are attempts to clarify the use of the substitution property in the proof and whether the angles can be considered supplementary based on the given conditions.

Discussion Status

The discussion is ongoing, with participants questioning the validity of certain steps in the proof and the application of geometric properties. Some guidance has been offered regarding the correct interpretation of the substitution property and the conditions under which angles are supplementary.

Contextual Notes

There is a noted confusion regarding the application of the substitution property and the necessity of using the converse of the theorem about supplementary angles and parallel lines. Participants are also addressing the importance of precise notation in geometric proofs.

Buzur
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Homework Statement


Given: AB \coprod CD ; \angleA \cong \angleC
Proof: AD \coprod BC
Geo Proof.png

Homework Equations



Idk how to necessary finish it...

The Attempt at a Solution



Statement -------------- Proof
1. AB \coprod CD ; \angleA \cong \angleC ----------- 1. Given
2. I say \angleA is supp. \angleD and \angleB is supp. \angleC ----------- 2. If two parallel lines cut by a transversal, then same-side interior angles are supp.

3. AD \coprod BC ---------------- 3. Substitution Prop.

Homework Statement

 
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I don't think you can prove that TRUE unless ∠ A = ∠ C exactly.
 
they are equal.. it was in the given information!
 
Buzur said:

Homework Statement


Given: AB \coprod CD ; \angleA \cong \angleC
Proof: AD \coprod BC


View attachment 51205


Homework Equations



Idk how to necessary finish it...


The Attempt at a Solution



Statement -------------- Proof
1. AB \coprod CD ; \angleA \cong \angleC ----------- 1. Given
2. I say \angleA is supp. \angleD and \angleB is supp. \angleC ----------- 2. If two parallel lines cut by a transversal, then same-side interior angles are supp.

3. AD \coprod BC ---------------- 3. Substitution Prop.

Homework Statement

What are you substuting into what? Are you saying you are substituting "AD"
for "AB" and "BC" for "CD" in the original statement? That's NOT what the "substitution prop." says! Nor can you simply substitute them into the theorem you stated about parallel lines and supplementary angles- you would need to use its converse which says that if a transversal cutting two lines forms supplementary angles then the lines are parallel.
 
Buzur said:
they are equal.. it was in the given information!

check your symbol... ≅
 

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